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Desynchronization and pattern formation in a noisy feed-forward oscillator network.

Clément Zankoc1,2,3, Duccio Fanelli1,2, Francesco Ginelli3

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Summary
This summary is machine-generated.

Small noise can disrupt synchronized oscillators through non-normal couplings, leading to complex spatiotemporal patterns. This noise-assisted instability destabilizes even advanced states like the splay state.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Statistical physics

Background:

  • Coupled oscillator systems exhibit synchronization phenomena.
  • Non-normal couplings can lead to amplification of perturbations.
  • Deterministic systems may lose synchrony under specific conditions.

Purpose of the Study:

  • Investigate the effect of small additive noise on diffusively coupled oscillators with non-normal couplings.
  • Analyze the mechanism of noise-assisted instability and pattern formation.
  • Characterize the asymptotic splay state and its stability.

Main Methods:

  • Analysis of a one-dimensional array of diffusively coupled oscillators.
  • Perturbation analysis with small additive noise.
  • Analytical characterization of attractors and stability.
  • Exploration of parameter regions for deterministic synchronization.

Main Results:

  • Non-normal couplings coherently amplify noise, causing instability.
  • Initial synchrony is lost, leading to an asymptotic splay state.
  • Noise-assisted instability destabilizes the splay state, generating spatiotemporal patterns.

Conclusions:

  • Non-normal couplings are crucial for noise-induced instability in oscillator arrays.
  • Conventional linear stability analysis fails to predict emergent spatiotemporal patterns.
  • The study reveals a novel mechanism for pattern formation driven by noise and non-normal dynamics.